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On the structure of dynamic principal component analysis used in statistical process monitoring
Luleå University of Technology, Department of Business Administration, Technology and Social Sciences, Business Administration and Industrial Engineering.
Luleå University of Technology, Department of Business Administration, Technology and Social Sciences, Business Administration and Industrial Engineering. Technical University of Denmark.
Luleå University of Technology, Department of Business Administration, Technology and Social Sciences, Business Administration and Industrial Engineering.ORCID iD: 0000-0003-3911-8009
2017 (English)In: Chemometrics and Intelligent Laboratory Systems, ISSN 0169-7439, E-ISSN 1873-3239, Vol. 167, 1-11 p.Article in journal (Refereed) Published
Abstract [en]

When principal component analysis (PCA) is used for statistical process monitoring it relies on the assumption that data are time independent. However, industrial data will often exhibit serial correlation. Dynamic PCA (DPCA) has been suggested as a remedy for high-dimensional and time-dependent data. In DPCA the input matrix is augmented by adding time-lagged values of the variables. In building a DPCA model the analyst needs to decide on (1) the number of lags to add, and (2) given a specific lag structure, how many principal components to retain. In this article we propose a new analyst driven method to determine the maximum number of lags in DPCA with a foundation in multivariate time series analysis. The method is based on the behavior of the eigenvalues of the lagged autocorrelation and partial autocorrelation matrices. Given a specific lag structure we also propose a method for determining the number of principal components to retain. The number of retained principal components is determined by visual inspection of the serial correlation in the squared prediction error statistic, Q (SPE), together with the cumulative explained variance of the model. The methods are illustrated using simulated vector autoregressive and moving average data, and tested on Tennessee Eastman process data.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 167, 1-11 p.
Keyword [en]
Dynamic principal component analysis, Vector autoregressive process, Vector moving average process, Autocorrelation, Simulation, Tennessee Eastman process simulator
National Category
Reliability and Maintenance
Research subject
Quality Technology and Management
Identifiers
URN: urn:nbn:se:ltu:diva-63377DOI: 10.1016/j.chemolab.2017.05.016ISI: 000408790200001Scopus ID: 2-s2.0-85019887093OAI: oai:DiVA.org:ltu-63377DiVA: diva2:1095953
Funder
Swedish Research Council, 340-2013-5108
Note

Validerad;2017;Nivå 2;2017-06-02 (rokbeg)

Available from: 2017-05-16 Created: 2017-05-16 Last updated: 2017-11-24Bibliographically approved

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Vanhatalo, ErikKulahci, MuratBergquist, Bjarne

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